#include <SparseGenComplexShiftSolve.h>

Public Types
using	Scalar = Scalar_

Public Member Functions
Index	cols () const

void	perform_op (const Scalar x_in, Scalar y_out) const

Index	rows () const

void	set_shift (const Scalar &sigmar, const Scalar &sigmai)

template<typename Derived >
	SparseGenComplexShiftSolve (const Eigen::SparseMatrixBase< Derived > &mat)

Private Types
using	Complex = std::complex< Scalar >

using	ComplexSolver = Eigen::SparseLU< SparseComplexMatrix >

using	ComplexVector = Eigen::Matrix< Complex, Eigen::Dynamic, 1 >

using	ConstGenericSparseMatrix = const Eigen::Ref< const SparseMatrix >

using	Index = Eigen::Index

using	MapConstVec = Eigen::Map< const Vector >

using	MapVec = Eigen::Map< Vector >

using	SparseComplexMatrix = Eigen::SparseMatrix< Complex, Flags, StorageIndex >

using	SparseMatrix = Eigen::SparseMatrix< Scalar, Flags, StorageIndex >

using	Vector = Eigen::Matrix< Scalar, Eigen::Dynamic, 1 >

Private Attributes
ConstGenericSparseMatrix	m_mat

const Index	m_n

ComplexSolver	m_solver

ComplexVector	m_x_cache

Detailed Description

template<typename Scalar_, int Flags = Eigen::ColMajor, typename StorageIndex = int>
class Spectra::SparseGenComplexShiftSolve< Scalar_, Flags, StorageIndex >

This class defines the complex shift-solve operation on a sparse real matrix $A$ , i.e., calculating $y=\mathrm{Re}\{(A-\sigma I)^{-1}x\}$ for any complex-valued $\sigma$ and real-valued vector $x$ . It is mainly used in the GenEigsComplexShiftSolver eigen solver.

Template Parameters

Scalar_	The element type of the matrix, for example, `float`, `double`, and `long double`.
Flags	Either `Eigen::ColMajor` or `Eigen::RowMajor`, indicating the storage format of the input matrix.
StorageIndex	The type of the indices for the sparse matrix.

Definition at line 32 of file SparseGenComplexShiftSolve.h.

Member Typedef Documentation

◆ Complex

template<typename Scalar_ , int Flags = Eigen::ColMajor, typename StorageIndex = int>

using Spectra::SparseGenComplexShiftSolve< Scalar_, Flags, StorageIndex >::Complex = std::complex<Scalar>

private

Definition at line 48 of file SparseGenComplexShiftSolve.h.

◆ ComplexSolver

template<typename Scalar_ , int Flags = Eigen::ColMajor, typename StorageIndex = int>

using Spectra::SparseGenComplexShiftSolve< Scalar_, Flags, StorageIndex >::ComplexSolver = Eigen::SparseLU<SparseComplexMatrix>

private

Definition at line 52 of file SparseGenComplexShiftSolve.h.

◆ ComplexVector

template<typename Scalar_ , int Flags = Eigen::ColMajor, typename StorageIndex = int>

using Spectra::SparseGenComplexShiftSolve< Scalar_, Flags, StorageIndex >::ComplexVector = Eigen::Matrix<Complex, Eigen::Dynamic, 1>

private

Definition at line 49 of file SparseGenComplexShiftSolve.h.

◆ ConstGenericSparseMatrix

template<typename Scalar_ , int Flags = Eigen::ColMajor, typename StorageIndex = int>

using Spectra::SparseGenComplexShiftSolve< Scalar_, Flags, StorageIndex >::ConstGenericSparseMatrix = const Eigen::Ref<const SparseMatrix>

private

Definition at line 46 of file SparseGenComplexShiftSolve.h.

◆ Index

template<typename Scalar_ , int Flags = Eigen::ColMajor, typename StorageIndex = int>

using Spectra::SparseGenComplexShiftSolve< Scalar_, Flags, StorageIndex >::Index = Eigen::Index

private

Definition at line 41 of file SparseGenComplexShiftSolve.h.

◆ MapConstVec

template<typename Scalar_ , int Flags = Eigen::ColMajor, typename StorageIndex = int>

using Spectra::SparseGenComplexShiftSolve< Scalar_, Flags, StorageIndex >::MapConstVec = Eigen::Map<const Vector>

private

Definition at line 43 of file SparseGenComplexShiftSolve.h.

◆ MapVec

template<typename Scalar_ , int Flags = Eigen::ColMajor, typename StorageIndex = int>

using Spectra::SparseGenComplexShiftSolve< Scalar_, Flags, StorageIndex >::MapVec = Eigen::Map<Vector>

private

Definition at line 44 of file SparseGenComplexShiftSolve.h.

◆ Scalar

template<typename Scalar_ , int Flags = Eigen::ColMajor, typename StorageIndex = int>

using Spectra::SparseGenComplexShiftSolve< Scalar_, Flags, StorageIndex >::Scalar = Scalar_

Element type of the matrix.

Definition at line 38 of file SparseGenComplexShiftSolve.h.

◆ SparseComplexMatrix

template<typename Scalar_ , int Flags = Eigen::ColMajor, typename StorageIndex = int>

using Spectra::SparseGenComplexShiftSolve< Scalar_, Flags, StorageIndex >::SparseComplexMatrix = Eigen::SparseMatrix<Complex, Flags, StorageIndex>

private

Definition at line 50 of file SparseGenComplexShiftSolve.h.

◆ SparseMatrix

template<typename Scalar_ , int Flags = Eigen::ColMajor, typename StorageIndex = int>

using Spectra::SparseGenComplexShiftSolve< Scalar_, Flags, StorageIndex >::SparseMatrix = Eigen::SparseMatrix<Scalar, Flags, StorageIndex>

private

Definition at line 45 of file SparseGenComplexShiftSolve.h.

◆ Vector

template<typename Scalar_ , int Flags = Eigen::ColMajor, typename StorageIndex = int>

using Spectra::SparseGenComplexShiftSolve< Scalar_, Flags, StorageIndex >::Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>

private

Definition at line 42 of file SparseGenComplexShiftSolve.h.

Constructor & Destructor Documentation

◆ SparseGenComplexShiftSolve()

template<typename Scalar_ , int Flags = Eigen::ColMajor, typename StorageIndex = int>

template<typename Derived >

Spectra::SparseGenComplexShiftSolve< Scalar_, Flags, StorageIndex >::SparseGenComplexShiftSolve ( const Eigen::SparseMatrixBase< Derived > & mat )

inline

Constructor to create the matrix operation object.

Parameters

mat	An Eigen sparse matrix object, whose type can be `Eigen::SparseMatrix<Scalar, ...>` or its mapped version `Eigen::Map<Eigen::SparseMatrix<Scalar, ...> >`.

Definition at line 68 of file SparseGenComplexShiftSolve.h.

Member Function Documentation

◆ cols()

template<typename Scalar_ , int Flags = Eigen::ColMajor, typename StorageIndex = int>

Index Spectra::SparseGenComplexShiftSolve< Scalar_, Flags, StorageIndex >::cols ( ) const

inline

Return the number of columns of the underlying matrix.

Definition at line 86 of file SparseGenComplexShiftSolve.h.

◆ perform_op()

template<typename Scalar_ , int Flags = Eigen::ColMajor, typename StorageIndex = int>

void Spectra::SparseGenComplexShiftSolve< Scalar_, Flags, StorageIndex >::perform_op	(	const Scalar *	x_in,
		Scalar *	y_out
	)		const

inline

Perform the complex shift-solve operation $y=\mathrm{Re}\{(A-\sigma I)^{-1}x\}$ .

Parameters

x_in	Pointer to the vector.
y_out	Pointer to the vector.

Definition at line 114 of file SparseGenComplexShiftSolve.h.

◆ rows()

template<typename Scalar_ , int Flags = Eigen::ColMajor, typename StorageIndex = int>

Index Spectra::SparseGenComplexShiftSolve< Scalar_, Flags, StorageIndex >::rows ( ) const

inline

Return the number of rows of the underlying matrix.

Definition at line 82 of file SparseGenComplexShiftSolve.h.

◆ set_shift()

template<typename Scalar_ , int Flags = Eigen::ColMajor, typename StorageIndex = int>

void Spectra::SparseGenComplexShiftSolve< Scalar_, Flags, StorageIndex >::set_shift	(	const Scalar &	sigmar,
		const Scalar &	sigmai
	)

inline

Set the complex shift $\sigma$ .

Parameters

sigmar	Real part of $\sigma$ .
sigmai	Imaginary part of $\sigma$ .

Definition at line 94 of file SparseGenComplexShiftSolve.h.

Member Data Documentation

◆ m_mat

template<typename Scalar_ , int Flags = Eigen::ColMajor, typename StorageIndex = int>

ConstGenericSparseMatrix Spectra::SparseGenComplexShiftSolve< Scalar_, Flags, StorageIndex >::m_mat

private

Definition at line 54 of file SparseGenComplexShiftSolve.h.

◆ m_n

template<typename Scalar_ , int Flags = Eigen::ColMajor, typename StorageIndex = int>

const Index Spectra::SparseGenComplexShiftSolve< Scalar_, Flags, StorageIndex >::m_n

private

Definition at line 55 of file SparseGenComplexShiftSolve.h.

◆ m_solver

template<typename Scalar_ , int Flags = Eigen::ColMajor, typename StorageIndex = int>

ComplexSolver Spectra::SparseGenComplexShiftSolve< Scalar_, Flags, StorageIndex >::m_solver

private

Definition at line 56 of file SparseGenComplexShiftSolve.h.

◆ m_x_cache

template<typename Scalar_ , int Flags = Eigen::ColMajor, typename StorageIndex = int>

ComplexVector Spectra::SparseGenComplexShiftSolve< Scalar_, Flags, StorageIndex >::m_x_cache

mutableprivate

Definition at line 57 of file SparseGenComplexShiftSolve.h.

The documentation for this class was generated from the following file:

SparseGenComplexShiftSolve.h

Public Types

Public Member Functions

Private Types

Private Attributes

Detailed Description

template<typename Scalar_, int Flags = Eigen::ColMajor, typename StorageIndex = int> class Spectra::SparseGenComplexShiftSolve< Scalar_, Flags, StorageIndex >

Member Typedef Documentation

◆ Complex

◆ ComplexSolver

◆ ComplexVector

◆ ConstGenericSparseMatrix

◆ Index

◆ MapConstVec

◆ MapVec

◆ Scalar

◆ SparseComplexMatrix

◆ SparseMatrix

◆ Vector

Constructor & Destructor Documentation

◆ SparseGenComplexShiftSolve()

Member Function Documentation

◆ cols()

◆ perform_op()

◆ rows()

◆ set_shift()

Member Data Documentation

◆ m_mat

◆ m_n

◆ m_solver

◆ m_x_cache

template<typename Scalar_, int Flags = Eigen::ColMajor, typename StorageIndex = int>
class Spectra::SparseGenComplexShiftSolve< Scalar_, Flags, StorageIndex >